Introduction to Liquid Crystals

The existence of liquid crystals has been known for nearly a centu­ ry; yet it is only in the last ten years that their unique optical, electri­ cal, electro-optic, and thermal properties have been exploited to any significant extent in such technological applications as digital d~­ plays and thermography. Digital watches equipped with liquid-crys­ tal displays (LCD's) have recently made their debut in the electronic watch market, and the large-scale use of LCD's in a variety of other applications requiring reliable, low-power digital displays is immi­ nent. There is good reason to believe that liquid crystals will be the first electro-optic materials to find widespread commercial use. Apart from applications, liquid crystals are unique among the phases of matter. Lurking beneath their garish display of color and texture is a great complexity of physical and chemical interaction that is only now beginning to unfold in the face of a decade-old resurgence in all aspects of liquid~rystal research. RCA Laboratories has participated in this resurgence from its beginning in the early 1960's and at present maintains active liquid-crystal programs both in basic re­ search and in device engineering. In view of the widespread interest in liquid crystals at RCA Labo­ ratories, an in-house weekly seminar devoted to the subject of liquid crystals was organized in the fall of 1973. The resulting lectures were subsequently published in three issues of the RCA Review and, with the incorporation of much additional material, eventually grew into the present volume.

1 Liquid Crystal Mesophases.- 1. Mesophases.- 1.1 Disordered Crystal Mesophases.- 1.2 Ordered Fluid Mesophases.- 2. Types of Liquid Crystals.- 2.1 Thermotropic Liquid Crystals.- 2.2 Lyotropic Liquid Crystals.- 3. Classification According to Molecular Order.- 3.1 Nematic Order.- 3.2 Cholesteric Order.- 3.3 Smectic Order.- 4. Polymorphism in Thermotropic Liquid Crystals.- 5. Molecular Structure of Thermotropic Mesogens.- 6. Properties of Ordered Fluid Mesophases.- 2 Structure-Property Relationships in Thermotropic Organic Liquid Crystals.- 1. Introduction.- 2. Organic Mesophases.- 3. General Structural Features of Mesogens.- 4. Effects of Structure on Mesophase Thermal Stability.- 5. Homologous Series.- 6. Materials for Device Applications.- 7. Summary.- 3 Introduction to the Molecular Theory of Nematic Liquid Crystals.- 1. Introduction.- 2. Symmetry and the Order Parameter.- 3. The Molecular Potential.- 4. The Orientational Distribution function.- 5. Thermodynamics of the Nematic Phase.- 6. Fluctuations at Tc.- 4 Generalized Mean Field Theory of Nematic Liquid Crystals.- 1. Introduction.- 2. The Pair Interaction Potential.- 3. The Mean Field Approximation.- 4. Statistical Thermodynamics.- 5. Nature of the Parameters UL.- 6. The Need for Higher Order Terms in V1.- 5 Hard Rod Model of the Nematic-Isotropic Phase Transition.- 1. Introduction.- 2. Derivation of Onsager Equations.- 3. Solution of Onsager Equations in a Simplified Case.- 6 Nematic Order: The Long Range Orientational Distribution Function.- 1. Introduction.- 2. The Orientational Distribution function.- 3. Macroscopic Definition of Nematic Order.- 4. Relationship Between Microscopic and Macroscopic Order Parameters.- 5. Experimental Measurements.- 5.1 Measurements of ?P2(cos ?)? Based on Macroscopic Anisotropies.- 5.2 Measurements of ?P2(cos ?)? Based on Microscopic Anisotropies.- 6. Experimental Data.- 7 Introduction to the Molecular Theory of Smectic-A Liquid Crystals.- 1. Introduction.- 2. Symmetry, Structure and Order Parameters.- 3. Phase Diagrams.- 4. The Molecular Potential.- 5. Statistical Thermodynamics.- 6. Numerical Results.- 7. Improved Theory.- 8. The Possibility of Second-Order Transitions.- 8 Introduction to the Elastic Continuum Theory of Liquid Crystals.- 1. Introduction.- 2. The Fundamental Equation of the Continuum Theory of Liquid Crystals.- 3. Applications of the Elastic Continuum Theory.- 3.1 Twisted Nematic Cell.- 3.2 Magnetic Coherence Length.- 3.3 Fréedericksz Transition.- 3.4 Field-Induced Cholesteric—Nematic Transition.- 4. Concluding Remarks.- 9 Electrohydrodynamic Instabilities in Nematic Liquid Crystals.- 1. Introduction.- 2. Nature of the Instability and the Balance of Forces.- 3. Dielectric Response.- 4. Hydrodynamic Effects.- 5. The Boundary Value Problem in the Conduction Regime.- 6. The Torque Balance Equation.- 7. Numerical Results and Comparison with Experiment.- 8. Range of Applicability.- 10 The Landau-de Gennes Theory of Liquid Crystal Phase Transitions.- 1. Introduction.- 2. Derivation of the Fundamental Equations of the Landau-de Gennes Theory.- 2.1 The Partition function.- 2.2 The Landau Expansion.- 2.3 Generalization of the Landau Expansion to Liquid Crystals.- 3. Thermodynamic Properties of Liquid Crystal Phase Transitions.- 4. Fluctuation Phenomena.- 4.1 Homophase Fluctuations in the Isotropic Phase.- 4.2 Heterophase Fluctuations.- 5. Observation of Fluctuations Using Light Scattering.- 6. Magnetic Birefringence and the Paranematic Susceptibility.- Appendix A.- Appendix B.- 11 Introduction to the Optical Properties of Cholesteric and Chiral Nematic Liquid Crystals.- 1. Introduction.- 2. Maxwell’s Equations.- 3. Discussion.- 4. Conclusion.- Appendix A.- Appendix B.- 12 Liquid-Crystal Displays—Packaging and Surface Treatments.- 1. Introduction.- 2. Packaging.- 3. Electrodes.- 4. Surface Orientation.- 5. Influence of Packaging on Surface Orientation.- 6. Summary.- 13 Pressure Effects in Sealed Liquid-Crystal Cells.- 1. Introduction.- 2. Effect of Temperature Change.- 3. Effect of Glass Thickness.- 4. The Case of a Rigid Container.- 14 Liquid-Crystal Displays—Electro-optic Effects and Addressing Techniques.- 1. Introduction.- 2. Electro-optic Phenomena.- 2.1 Field-Induced Birefringence.- 2.2 Twisted Nematic Effect.- 2.3 Guest-Host Effect.- 2.4 Cholesteric-to-Nematic Transition.- 2.5 Dynamic Scattering.- 2.6 Storage Mode.- 2.7 Transient Response.- 3. Display-Related Parameters.- 3.1 Display Life.- 3.2 Temperature Dependence.- 4. Addressing Techniques.- 4.1 Matrix Addressing.- 4.2 Beam Scanning.- 5. Summary.- 15 Liquid-Crystal Optical Waveguides.- 1. Introduction.- 2. Guided Optical Waves.- 3. Phase Matching and Coupling.- 4. Scattering.- 5. Liquid Crystal Waveguides.- 6. Conclusions.- 16 The Electro-optic Transfer Function in Nematic Liquids.- 1. Introduction.- 2. Geometrical Considerations in Optical Measurements.- 3. Field Effects—Negative Dielectric Anisotropy.- 4. Field Effects—Positive Dielectric Anisotropy.- 5. Hydrodynamic Effects—Diffraction by Domains.- 6. Dynamic Scattering.- 7. Photoconductor Control.- 17 Electrochemistry in Nematic Liquid-Crystal Solvents.- 1. Introduction.- 2. Equilibrium Properties of Bulk Solutions.- 3. Electrochemical Reactions.- 18 Lyotropic Liquid Crystals and Biological Membranes: The Crucial Role of Water.- 1. Introduction.- 2. Lyotropic Liquid Crystals.- 2.1 Constituents of Lyotropics.- 2.2 Micelles.- 2.3 Structure of Lyotropics.- 3. Biological Membranes.- 3.1 Constituents of Membranes.- 3.2 Structures of Membranes.- 4. Interaction of Amphiphilic Compounds with Water.- 4.1 Solubility of Hydrocarbons in Water.- 4.2 Solubility of Ionized Species in Water.- 4.3 Aggregation of Amphiphilic Compounds.- 5. Conclusion.